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DOI:
Journal of Software:2006.17(4):713-719

子共代数与共同余共关系
周晓聪,舒忠梅
(中山大学,计算机科学系,广东,广州,510275)
Subcoalgebras and Cocongruence Corelations
ZHOU Xiao-Cong,SHU Zhong-Mei
()
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Received:March 01, 2005    Revised:October 10, 2005
> 中文摘要: 共代数方法是近几年来理论计算机科学的研究热点之一,在并行计算模型、自动机及面向对象技术的理论基础方面有着广泛的应用.以范畴理论为工具讨论子共代数的性质,特别是集合范畴上的子共代数的性质,证明了集合范畴上的子共代数都是正则子共代数.进一步利用共同余共关系与子共代数之间的对应,给出了集合范畴上共生成子共代数的一种构造方式.
中文关键词: 共代数  子共代数  共关系  范畴理论
Abstract:The study of coalgebraic methods, as one of the active areas for theoretical computer science in recent years, is widely used in concurrence computing model, automat theory, and the foundations of object-oriented technology. Through using category theory, this paper investigates the properties of subcoalgebras, especially, the properties of subcoalgebras on Set, the category of sets and functions. This paper shows that all the subcoalgebras on Set are regular. Furthermore, using the correspondence between the cocongruence corelations and the subcoalgebras on Set, a way to construct the co-generated subcoalgebra is given in this paper.
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基金项目:Supported by the National Natural Science Foundation of China under Grant No.60403013 (国家自然科学基金); the Natural Science Foundation of Guangdong Province of China under Grant No.031542 (广东省自然科学基金) Supported by the National Natural Science Foundation of China under Grant No.60403013 (国家自然科学基金); the Natural Science Foundation of Guangdong Province of China under Grant No.031542 (广东省自然科学基金)
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周晓聪,舒忠梅.子共代数与共同余共关系.软件学报,2006,17(4):713-719

ZHOU Xiao-Cong,SHU Zhong-Mei.Subcoalgebras and Cocongruence Corelations.Journal of Software,2006,17(4):713-719